Explain with reasons :
A. Transition elements show variable oxidation states.
B. Transition elements form colored compounds.
C. The size of lanthanide elements decreases from La to Lu.

Hint: As we know that the transition element is an element whose atom consists of a moderately filled subshell, which may give rise to the cation with an incomplete D subshell.
The lanthanide or lanthanoid chain of chemical elements consists of \[15\]metallic chemical elements with atomic number \[57 - 71\] from lanthanum through lutetium. These elements with chemically similar elements scandium and yttrium, are often known as rare earth elements.

Complete answer: or Complete step by step answer:
A transition element is an element of the D-block of the periodic table which includes groups of \[3to12\]. In actual practice, the f-block lanthanide and actinide series are also considered transition metals and are called “internal transition metals” .
Mercury, cadmium and zinc are not considered as a transition element because of their electronic configuration which corresponds to \[(n - 1){d^{10}}n{s^2}\] . Some elements have coloured compounds and ions. Its colour is explained by the d-d transition of electrons.
Transition elements have variable state oxidation in their compound because there is very less Energy difference between \[(n - 1)d\] and ns orbitals.
Accordingly, electrons of \[(n - 1)d\] orbitals and ns orbitals take part in bond manufacturing.
\[Mn(z - 25)\] have the maximum number of unpaired electrons present in the d-subshell . So , this is the maximum oxidation state \[( + 7)\] .
Transition elements form coloured compounds because they have half filled orbitals . There is crystal field theory which describes the breaking of the orbital . There is a continuous decrease of atom positive size or ionic La from the ion of positive lanthanide ions to atom charge or electron entering the internal \[(n - 2)\]f orbital .

Note:
This gradual decrease in size with increasing atomic number is called Lanthanide contraction.
The colours of lanthanide complexes are almost entirely derived from charge transfer interactions between the metal and the ligand.